Why partial derivatives in continuity equation?

Why is partial derivative with respect to time used in the continuity equation,
[tex]
\frac{\partial \rho}{\partial t} = - \nabla \vec{j}
[/tex]
If this equation is really derived from the equation,
[tex]
\frac{dq}{dt} = - \int\int \vec{j} \cdot d\vec{a}
[/tex]
Then should it be a total derivative with respect to time?